Week 1: Fundamentals; approximations
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Week 9: Order statistics; beta family; conjugate priors
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Week 2: Random variables, discrete and continuous
distributions and joint distributions
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Week 10: Conditional expectation; variance by conditioning;
least squares
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Week 3: Conditioning and independence; random counts; Poisson
limit
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Week 11: Random vectors;
multivariate normal; linear combinations; independence
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Week 4: Expectation and SD; bounds
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Week 12:
Simple linear regression; correlation and cosines; regression effect
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Week 5: Sample sums; Weak Law; Central Limit Theorem and the
normal distribution
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Week 13:
Conditioning and the multivariate normal; multiple regression
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Week 6: Change of variable for joint densities; distributions
of sums
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Week 14: Intro to Markov Chains
(Thanksgiving Break)
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Week 7: Generating functions; Chernoff's bound; CLT via mgf's
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Week 15: Long run behavior; hidden Markov models (or MCMC)
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Week 8: Poisson process; Midterm Friday October 12
during lab
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Week 16: RRR
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